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The five-time Ballon d'Or winner's attitude has been called into question after he threw a strop when Rangnick substituted him in the 3-1 win over Brentford on Wednesday night.
But behind closed doors, Ronaldo was also not happy with another decision made by Manchester United's interim boss.
In a detailed report from The Athletic, it's claimed the 36-year-old was not doing the business for his team during an 11-a-side training drill.
He had been leading the line in attack but Rangnick decided to switch him to the left flank, a position he played with distinction during his first spell at Old Trafford.
But it's said Ronaldo was "nearly affronted" at the request from Rangnick - even if the tweak worked as he finished the training session strongly.
According to the same outlet, Ronaldo annoyed some of his teammates with his recent call out of United's young players in an interview.
During with a chat with Sky Sports, the Portuguese superstar said: "If I give you advice, even if you are younger than me, but if that's not in your plan during your daily life then it will be difficult.
"You can speak all day with that person, but if it's not coming from inside of you then it is impossible.
"I remember when I was 18, 19, 20, some older players spoke with me, but I put that as: 'Cristiano, you have to improve — they know more than you, they are more experienced than you, they passed through many bad moments.'
"But the other people do not accept that if you criticise them - I don't say this generation of our players but in general, I have kids, I know.
"Sometimes when you're a little bit harder, they do the opposite, so you have to find the right balance to speak with them."
The report goes on to state that younger members of the squad feel Ronaldo is difficult to talk to.
They would feel more confident speaking to Edinson Cavani, as despite his English being far from perfect, he appears more approachable.
Ronaldo has 14 goals in all competitions since sealing a dream return to United.
But at the same time, the former Real Madrid and Juventus man has regularly stormed down the tunnel after games and displayed worrying body language.
After Ronaldo failed to hide his fury vs Brentford, Rangnick explained he told the No.7 he "had to take the decision for the team, for the club".